Reversible data hiding (RDH) techniques applied on military, medical, and legal fields have been broadly presented in the recent years. Some prediction-error expansion (PEE) based methods based on the modification of two-dimensional prediction-error histogram (2D PEH) exploit image redundancy to obtain correlation among prediction-errors. In this work, a novel RDH method called 4-wise PEE over 2D PEH framework is presented here. The 4-wise PEE can make use of image redundancy to get better correlation. First, regarding every four adjacent prediction-errors as a unit, we acquire a new sequence consisted of prediction-errors quaternities; then, a four-dimensional prediction-error histogram (4D PEH) is also generated. Finally, secret messages are embedded into the cover image utilizing 4-wise PEE.